2. A company is considering building a bridge across a river. The bridge would cost $2 million to build and nothing to maintain. The following table shows the company¡¯s anticipated demand over the lifetime of the bridge:
Price per crossing ($) 8 7 6 5 4 3 2 1 0
Number of crossings (¡®000) 0 100 200 300 400 500 600 700 800
a. If the company were to build the bridge, what would be its profit-maximizing price? Would that be the efficient level of output? Why or why not?
b. If the company is interested in maximizing profit, should it build the bridge? What would be its profit or loss?
c. If the government were to build the bridge, what price should it charge?
d. Should the government build the bridge? Explain your answer.
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a. To determine the profit-maximizing price, we need to calculate the total revenue and total cost at each price level. The total revenue is calculated by multiplying the price per crossing by the number of crossings, and the total cost is the cost of building the bridge.
Price | Number of Crossings | Total Revenue | Total Cost
------|-------------------|---------------|-----------
8 | 0 | 0 | 2,000,000
7 | 100 | 700,000 | 2,000,000
6 | 200 | 1,200,000 | 2,000,000
5 | 300 | 1,500,000 | 2,000,000
4 | 400 | 1,600,000 | 2,000,000
3 | 500 | 1,500,000 | 2,000,000
2 | 600 | 1,200,000 | 2,000,000
1 | 700 | 700,000 | 2,000,000
0 | 800 | 0 | 2,000,000
From the table, we can see that the company's profit is the highest when the price is $4, as it has the lowest total cost and still generates significant revenue. However, this price level does not correspond to an efficient level of output because the marginal cost for each additional crossing is zero (no maintenance costs). The efficient level of output would be where the price equals marginal cost, which in this case would be $0.
b. If the company is interested in maximizing profit, it should build the bridge and set the price at $4. At this price, the company would generate a profit of $1,600,000 ($1,600,000 in revenue - $2,000,000 in costs).
c. If the government were to build the bridge, it should charge the price equal to the marginal cost of crossing, which is $0. Setting the price at this level would lead to an efficient allocation of resources and encourage the maximum number of crossings.
d. Whether the government should build the bridge depends on its objective. If the government's goal is to maximize social welfare and overall economic efficiency, then it should build the bridge and set the price at $0. However, if the government's goal is to generate revenue or cover the costs of construction, then it may not be economically feasible to build the bridge. Additionally, other factors such as the potential benefits to the local community, environmental impacts, and other investment opportunities should also be considered before making a decision.
To determine the profit-maximizing price for the company in building the bridge, we can analyze the data in the table provided. The profit of the company can be calculated by subtracting the total cost from the total revenue.
a. To identify the profit-maximizing price, we need to calculate the total revenue and total cost associated with each potential price. The total revenue is equal to the price per crossing multiplied by the number of crossings. The total cost is $2 million, as mentioned in the question.
To find the profit at each price, we subtract the cost from the revenue. The profit for each price is calculated using the formula: profit = (price per crossing * number of crossings) - $2 million.
Using this formula, we can calculate the profit at each price level:
Price per crossing ($) 8 7 6 5 4 3 2 1 0
Number of crossings (‘000) 0 100 200 300 400 500 600 700 800
Profit ($) -2000 -300 2500 6000 8500 9000 7400 4200 0
From the table, we can observe that the maximum profit is obtained at a price of $4 per crossing, resulting in a profit of $8,500. This is the profit-maximizing price for the company.
However, this may not necessarily be the efficient level of output. Efficiency is achieved when resources are allocated in a manner that maximizes overall social welfare or benefit. In this case, the efficient level of output should be determined by considering factors such as the value or demand of the bridge to society as a whole.
b. To determine whether the company should build the bridge in order to maximize profit, we need to compare the potential profit with the cost of building the bridge. Since the cost of construction is $2 million, we need to evaluate if the potential profit is higher than this cost.
At the profit-maximizing price of $4 per crossing, the company would have a profit of $8,500. This amount is higher than the construction cost of $2 million. Therefore, if the company is solely interested in maximizing profit, it should build the bridge. The profit (revenue - cost) for the company in this case would be $8,500 minus $2 million, resulting in a total profit of $6,500.
c. If the government were to build the bridge, the price it should charge depends on its objectives. The government may aim to achieve different goals, such as maximizing social welfare or minimizing costs for users. If the government aims to recover the cost of building the bridge, it could set the price equal to the construction cost divided by the estimated number of crossings over the bridge's lifetime. In this case, it would be $2 million divided by 800, resulting in a price of $2,500 per crossing.
d. Whether the government should build the bridge depends on various factors, including the expected benefits and costs associated with the project. If the estimated social benefits, such as reduced congestion or improved accessibility, exceed the costs (including construction and maintenance), it may be economically justified for the government to build the bridge. Additionally, if private companies are not willing to invest in the bridge due to market uncertainties or limitations, government intervention could be considered to ensure public access to vital infrastructure.